On “Computational Complexity and Information Asymmetry in Financial Products”
Sanjeev Arora, Boaz Barak, Markus Brunnermeier, Rong Ge
Communications of the ACM, 2011, May; v. 54, #5
More generally, in computational complexity we consider a computational task infeasible if the resources needed to solve it grow exponentially in the length of the input, and consider it feasible if these resources only grow polynomially in the input length.
Arghhh!!
No! It is not it asymptotic behavior that thwarts, it is the actual size of the computation we must do.
“We do not live in Asymptopia!”
… yet even a sophisticated investor like Goldman Sachs would have no idea what to pay for it.
I grant the point.
The simple answer is for Goldman Sachs to not buy the derivative.
I am not far into the paper so this comment may be unwarranted but lest I forget I record it now:
We do not need an algorithm to price a derivative, we merely need an algorithm to verify that a particular derivative is safe, where ‘safe’ is to be defined by the algorithm designer.
Safety must also be a property that legitimate derivative producers can reasonably conform their products to.
This fits the game theory model where the game is between the buyer and seller.
I suspect that legitimate market requirements are compatible with some such safety definition.
I may be wrong however.
By ‘safe’ I do not mean ‘certain not to lose money’.
The person selling the derivative can structure (“rig”) the derivative in a way such that it has low yield, but distinguishing it from a normal (“unrigged”) higher yield derivative is computationally intractable. Thus any efficient pricing mechanism would either overvalue the rigged derivative or undervalue the unrigged one, hence creating an inefficiency in the market.
I grant this too.
The question is whether we can we incent the derivative producer to construct transparent derivatives, without forgoing some legitimate end.
The sellers have no business unless they can find buyers and if buyers refuse opaque derivatives they will have to produce transparent derivatives.
If some buyers buy opaque derivatives then they will eventually fail but this process can be slow and we have the classic short-term vs. long-term dilemma.
Rating agencies need a new rating parameter: “opacity”.
At this point I think that the authors have asked the wrong question, but I will read on for a while.
As I read farther I begin to suspect that some legitimate forces may lead to opacity.
It is not trivial.
I was unaware of DeMarzo’s Theorem.
I think that the authors are addressing a different and interesting problem.
They address asymmetry of information by the tranche logic which can be roughly described as insuring repayment under normal failure rates.